task_name
stringclasses
6 values
strategy_id
stringclasses
20 values
input_text
stringlengths
6
26
reasoning_trace
stringlengths
11
152
linear_equation_solving
linear_equation_solving:subtract-then-divide
8x-56=-112
8x-56=-112 ; 8x=-56 ; x=-7
base_conversion
base_conversion:via-binary
n=28,base=8
BINLEN:5 ; CHUNK:0:3 ; CHUNK:1:4 ; OUT:34
linear_equation_solving
linear_equation_solving:subtract-then-divide
3x-21=-18
3x-21=-18 ; 3x=3 ; x=1
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(1,2) ; G=(5,4)
R:(1,3) ; D:(2,3) ; R:(2,4) ; D:(3,4) ; D:(4,4) ; D:(5,4)
list_summation
list_summation:left-to-right
2, 7, 9, 5
2+7=9 ; 9+9=18 ; 18+5=23
list_summation
list_summation:right-to-left
7, 0, 3, 4
3+4=7 ; 0+7=7 ; 7+7=14
base_conversion
base_conversion:repeated-division
n=10,base=2
DIV:10/2=5,r:0 ; DIV:5/2=2,r:1 ; DIV:2/2=1,r:0 ; DIV:1/2=0,r:1 ; OUT:1010
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(4,3) ; G=(5,4)
D:(5,3) ; R:(5,4)
linear_equation_solving
linear_equation_solving:subtract-then-divide
9x+18=36
9x+18=36 ; 9x=18 ; x=2
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(0,0) ; G=(4,2)
D:(1,0) ; D:(2,0) ; D:(3,0) ; D:(4,0) ; R:(4,1) ; R:(4,2)
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(4,2) ; G=(5,3)
R:(4,3) ; D:(5,3)
linear_equation_solving
linear_equation_solving:inverse-ops
2x+0=-14
2x+0=-14 ; x=(-14-0)/2 ; x=-14/2 ; x=-7
multidigit_addition
multidigit_addition:rounding-decomposition
783+806
round:790+806=1596 ; adjust:1596-7=1589 ; sum=1589
base_conversion
base_conversion:via-binary
n=204,base=4
BINLEN:8 ; CHUNK:0:3 ; CHUNK:1:0 ; CHUNK:2:3 ; CHUNK:3:0 ; OUT:3030
linear_equation_solving
linear_equation_solving:subtract-then-divide
2x-18=-34
2x-18=-34 ; 2x=-16 ; x=-8
linear_equation_solving
linear_equation_solving:inverse-ops
7x-21=21
7x-21=21 ; x=(21--21)/7 ; x=42/7 ; x=6
multidigit_addition
multidigit_addition:rounding-decomposition
705+222
round:710+222=932 ; adjust:932-5=927 ; sum=927
linear_equation_solving
linear_equation_solving:inverse-ops
4x-36=-20
4x-36=-20 ; x=(-20--36)/4 ; x=16/4 ; x=4
sorting_algorithms
sorting_algorithms:merge-sort
8, 7, 6, 5, 0
[7,8,6,5,0] ; [7,8,5,6,0] ; [5,6,7,8,0] ; [0,5,6,7,8]
list_summation
list_summation:pairwise
1, 5, 5, 7
1+5=6 ; 5+7=12 ; 6+12=18
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(4,3) ; G=(5,4)
R:(4,4) ; D:(5,4)
list_summation
list_summation:right-to-left
8, 5, 9, 8
9+8=17 ; 5+17=22 ; 8+22=30
linear_equation_solving
linear_equation_solving:subtract-then-divide
3x+9=24
3x+9=24 ; 3x=15 ; x=5
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(2,0) ; G=(3,4)
D:(3,0) ; R:(3,1) ; R:(3,2) ; R:(3,3) ; R:(3,4)
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(0,0) ; G=(4,1)
D:(1,0) ; D:(2,0) ; D:(3,0) ; D:(4,0) ; R:(4,1)
linear_equation_solving
linear_equation_solving:divide-then-subtract
3x+21=42
3x+21=42 ; x+7=14 ; x=14-7 ; x=7
multidigit_addition
multidigit_addition:rounding-decomposition
311+504
round:320+504=824 ; adjust:824-9=815 ; sum=815
list_summation
list_summation:pairwise
9, 9, 8, 1
9+9=18 ; 8+1=9 ; 18+9=27
multidigit_addition
multidigit_addition:right-to-left-carry
505+942
d2:5+2+0=7→w7,c0 ; d1:0+4+0=4→w4,c0 ; d0:5+9+0=14→w4,c1 ; sum=1447
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(1,0) ; G=(4,5)
D:(2,0) ; D:(3,0) ; D:(4,0) ; R:(4,1) ; R:(4,2) ; R:(4,3) ; R:(4,4) ; R:(4,5)
sorting_algorithms
sorting_algorithms:selection-sort
1, 3, 8, 6, 0
[0,3,8,6,1] ; [0,1,8,6,3] ; [0,1,3,6,8] ; [0,1,3,6,8]
linear_equation_solving
linear_equation_solving:inverse-ops
7x-42=-7
7x-42=-7 ; x=(-7--42)/7 ; x=35/7 ; x=5
multidigit_addition
multidigit_addition:left-to-right-partials
953+207
p100:900+200=1100 ; p10:50+0=50 ; p1:3+7=10 ; sum=1100+50+10=1160
multidigit_addition
multidigit_addition:right-to-left-carry
529+142
d2:9+2+0=11→w1,c1 ; d1:2+4+1=7→w7,c0 ; d0:5+1+0=6→w6,c0 ; sum=671
multidigit_addition
multidigit_addition:rounding-decomposition
287+913
round:290+913=1203 ; adjust:1203-3=1200 ; sum=1200
linear_equation_solving
linear_equation_solving:divide-then-subtract
5x+15=60
5x+15=60 ; x+3=12 ; x=12-3 ; x=9
base_conversion
base_conversion:decomposition
n=140,base=2
TERM:1*2^7=128 ; TERM:0*2^6=0 ; TERM:0*2^5=0 ; TERM:0*2^4=0 ; TERM:1*2^3=8 ; TERM:1*2^2=4 ; TERM:0*2^1=0 ; TERM:0*2^0=0 ; OUT:10001100
base_conversion
base_conversion:decomposition
n=102,base=2
TERM:1*2^6=64 ; TERM:1*2^5=32 ; TERM:0*2^4=0 ; TERM:0*2^3=0 ; TERM:1*2^2=4 ; TERM:1*2^1=2 ; TERM:0*2^0=0 ; OUT:1100110
list_summation
list_summation:pairwise
1, 2, 9, 1
1+2=3 ; 9+1=10 ; 3+10=13
linear_equation_solving
linear_equation_solving:subtract-then-divide
5x-15=-50
5x-15=-50 ; 5x=-35 ; x=-7
list_summation
list_summation:pairwise
9, 0, 9, 2
9+0=9 ; 9+2=11 ; 9+11=20
linear_equation_solving
linear_equation_solving:subtract-then-divide
5x-25=-25
5x-25=-25 ; 5x=0 ; x=0
multidigit_addition
multidigit_addition:right-to-left-carry
763+186
d2:3+6+0=9→w9,c0 ; d1:6+8+0=14→w4,c1 ; d0:7+1+1=9→w9,c0 ; sum=949
list_summation
list_summation:left-to-right
4, 9, 7, 5
4+9=13 ; 13+7=20 ; 20+5=25
list_summation
list_summation:right-to-left
1, 9, 4, 5
4+5=9 ; 9+9=18 ; 1+18=19
multidigit_addition
multidigit_addition:right-to-left-carry
520+765
d2:0+5+0=5→w5,c0 ; d1:2+6+0=8→w8,c0 ; d0:5+7+0=12→w2,c1 ; sum=1285
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(4,3) ; G=(5,4)
R:(4,4) ; D:(5,4)
base_conversion
base_conversion:via-binary
n=58,base=16
BINLEN:6 ; CHUNK:0:3 ; CHUNK:1:10 ; OUT:3A
sorting_algorithms
sorting_algorithms:merge-sort
9, 4, 6, 7, 5
[4,9,6,7,5] ; [4,6,7,9,5] ; [4,5,6,7,9]
base_conversion
base_conversion:repeated-division
n=99,base=8
DIV:99/8=12,r:3 ; DIV:12/8=1,r:4 ; DIV:1/8=0,r:1 ; OUT:143
list_summation
list_summation:right-to-left
0, 3, 0, 0
0+0=0 ; 3+0=3 ; 0+3=3
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(4,2) ; G=(5,3)
R:(4,3) ; D:(5,3)
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(4,2) ; G=(5,4)
R:(4,3) ; D:(5,3) ; R:(5,4)
list_summation
list_summation:pairwise
0, 9, 9, 7
0+9=9 ; 9+7=16 ; 9+16=25
sorting_algorithms
sorting_algorithms:selection-sort
9, 7, 2, 5, 6
[2,7,9,5,6] ; [2,5,9,7,6] ; [2,5,6,7,9] ; [2,5,6,7,9]
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(2,2) ; G=(3,3)
R:(2,3) ; D:(3,3)
base_conversion
base_conversion:decomposition
n=49,base=8
TERM:6*8^1=48 ; TERM:1*8^0=1 ; OUT:61
multidigit_addition
multidigit_addition:rounding-decomposition
234+493
round:240+493=733 ; adjust:733-6=727 ; sum=727
base_conversion
base_conversion:decomposition
n=52,base=4
TERM:3*4^2=48 ; TERM:1*4^1=4 ; TERM:0*4^0=0 ; OUT:310
sorting_algorithms
sorting_algorithms:insertion-sort
5, 6, 8, 7, 0
[5,6,8,7,0] ; [5,6,8,7,0] ; [5,6,7,8,0] ; [0,5,6,7,8]
multidigit_addition
multidigit_addition:rounding-decomposition
324+319
round:330+319=649 ; adjust:649-6=643 ; sum=643
list_summation
list_summation:right-to-left
9, 6, 3, 2
3+2=5 ; 6+5=11 ; 9+11=20
linear_equation_solving
linear_equation_solving:inverse-ops
9x-63=-63
9x-63=-63 ; x=(-63--63)/9 ; x=0/9 ; x=0
sorting_algorithms
sorting_algorithms:bubble-sort
0, 8, 2, 9, 3
[0,2,8,9,3] ; [0,2,8,3,9] ; [0,2,3,8,9]
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(2,4) ; G=(4,5)
R:(2,5) ; D:(3,5) ; D:(4,5)
sorting_algorithms
sorting_algorithms:bubble-sort
2, 1, 7, 5, 3
[1,2,7,5,3] ; [1,2,5,7,3] ; [1,2,5,3,7] ; [1,2,3,5,7]
list_summation
list_summation:left-to-right
7, 4, 1, 7
7+4=11 ; 11+1=12 ; 12+7=19
list_summation
list_summation:right-to-left
8, 8, 1, 5
1+5=6 ; 8+6=14 ; 8+14=22
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(2,3) ; G=(5,4)
R:(2,4) ; D:(3,4) ; D:(4,4) ; D:(5,4)
sorting_algorithms
sorting_algorithms:bubble-sort
6, 0, 9, 5, 4
[0,6,9,5,4] ; [0,6,5,9,4] ; [0,6,5,4,9] ; [0,5,6,4,9] ; [0,5,4,6,9] ; [0,4,5,6,9]
multidigit_addition
multidigit_addition:right-to-left-carry
995+858
d2:5+8+0=13→w3,c1 ; d1:9+5+1=15→w5,c1 ; d0:9+8+1=18→w8,c1 ; sum=1853
multidigit_addition
multidigit_addition:right-to-left-carry
805+205
d2:5+5+0=10→w0,c1 ; d1:0+0+1=1→w1,c0 ; d0:8+2+0=10→w0,c1 ; sum=1010
list_summation
list_summation:pairwise
4, 8, 5, 0
4+8=12 ; 5+0=5 ; 12+5=17
linear_equation_solving
linear_equation_solving:subtract-then-divide
7x-28=7
7x-28=7 ; 7x=35 ; x=5
list_summation
list_summation:right-to-left
3, 9, 7, 4
7+4=11 ; 9+11=20 ; 3+20=23
sorting_algorithms
sorting_algorithms:heap-sort
3, 5, 2, 8, 7
[3,8,2,5,7] ; [8,3,2,5,7] ; [8,7,2,5,3] ; [3,7,2,5,8] ; [7,3,2,5,8] ; [7,5,2,3,8] ; [3,5,2,7,8] ; [5,3,2,7,8] ; [2,3,5,7,8] ; [3,2,5,7,8] ; [2,3,5,7,8]
multidigit_addition
multidigit_addition:right-to-left-carry
502+613
d2:2+3+0=5→w5,c0 ; d1:0+1+0=1→w1,c0 ; d0:5+6+0=11→w1,c1 ; sum=1115
multidigit_addition
multidigit_addition:left-to-right-partials
497+127
p100:400+100=500 ; p10:90+20=110 ; p1:7+7=14 ; sum=500+110+14=624
list_summation
list_summation:left-to-right
2, 5, 0, 4
2+5=7 ; 7+0=7 ; 7+4=11
sorting_algorithms
sorting_algorithms:bubble-sort
7, 4, 1, 6, 3
[4,7,1,6,3] ; [4,1,7,6,3] ; [4,1,6,7,3] ; [4,1,6,3,7] ; [1,4,6,3,7] ; [1,4,3,6,7] ; [1,3,4,6,7]
list_summation
list_summation:pairwise
9, 3, 4, 8
9+3=12 ; 4+8=12 ; 12+12=24
grid_pathfinding
grid_pathfinding:right-first
grid=6 ; S=(3,3) ; G=(4,4)
R:(3,4) ; D:(4,4)
linear_equation_solving
linear_equation_solving:subtract-then-divide
9x+45=-27
9x+45=-27 ; 9x=-72 ; x=-8
base_conversion
base_conversion:decomposition
n=158,base=4
TERM:2*4^3=128 ; TERM:1*4^2=16 ; TERM:3*4^1=12 ; TERM:2*4^0=2 ; OUT:2132
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(4,4) ; G=(5,5)
D:(5,4) ; R:(5,5)
multidigit_addition
multidigit_addition:left-to-right-partials
633+212
p100:600+200=800 ; p10:30+10=40 ; p1:3+2=5 ; sum=800+40+5=845
multidigit_addition
multidigit_addition:rounding-decomposition
285+373
round:290+373=663 ; adjust:663-5=658 ; sum=658
base_conversion
base_conversion:decomposition
n=72,base=8
TERM:1*8^2=64 ; TERM:1*8^1=8 ; TERM:0*8^0=0 ; OUT:110
grid_pathfinding
grid_pathfinding:alternating
grid=6 ; S=(2,3) ; G=(4,5)
R:(2,4) ; D:(3,4) ; R:(3,5) ; D:(4,5)
base_conversion
base_conversion:via-binary
n=212,base=2
BINLEN:8 ; CHUNK:0:1 ; CHUNK:1:1 ; CHUNK:2:0 ; CHUNK:3:1 ; CHUNK:4:0 ; CHUNK:5:1 ; CHUNK:6:0 ; CHUNK:7:0 ; OUT:11010100
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(3,2) ; G=(5,5)
D:(4,2) ; D:(5,2) ; R:(5,3) ; R:(5,4) ; R:(5,5)
multidigit_addition
multidigit_addition:left-to-right-partials
792+376
p100:700+300=1000 ; p10:90+70=160 ; p1:2+6=8 ; sum=1000+160+8=1168
list_summation
list_summation:left-to-right
4, 6, 9, 7
4+6=10 ; 10+9=19 ; 19+7=26
sorting_algorithms
sorting_algorithms:merge-sort
1, 3, 0, 6, 9
[0,1,3,6,9]
multidigit_addition
multidigit_addition:left-to-right-partials
758+739
p100:700+700=1400 ; p10:50+30=80 ; p1:8+9=17 ; sum=1400+80+17=1497
sorting_algorithms
sorting_algorithms:heap-sort
9, 7, 6, 8, 0
[9,8,6,7,0] ; [0,8,6,7,9] ; [8,0,6,7,9] ; [8,7,6,0,9] ; [0,7,6,8,9] ; [7,0,6,8,9] ; [6,0,7,8,9] ; [0,6,7,8,9]
grid_pathfinding
grid_pathfinding:down-first
grid=6 ; S=(4,0) ; G=(5,1)
D:(5,0) ; R:(5,1)
linear_equation_solving
linear_equation_solving:subtract-then-divide
7x-49=-28
7x-49=-28 ; 7x=21 ; x=3
sorting_algorithms
sorting_algorithms:bubble-sort
8, 2, 9, 3, 1
[2,8,9,3,1] ; [2,8,3,9,1] ; [2,8,3,1,9] ; [2,3,8,1,9] ; [2,3,1,8,9] ; [2,1,3,8,9] ; [1,2,3,8,9]
linear_equation_solving
linear_equation_solving:divide-then-subtract
5x-35=-60
5x-35=-60 ; x+-7=-12 ; x=-12--7 ; x=-5